Position-space renormalization-group approach for driven diffusive systems applied to the asymmetric exclusion model

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability $\alpha$ that a particle will flow into the chain to the leftmost site, the probability $\beta$ that a particle will flow out from the rightmost site, and the probability p that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system’s dynamics. The method yields a critical point at ${\alpha }_c={\beta }_c=1/2,$ in agreement with the exact values, and the critical exponent $\nu =2.71,$ as compared with the exact value $\nu =\mathrm{2.00.}\mathrm{}$